A constructive method for feedback stabilization of affine control systems with input and state constraints

The problem of synthesis of a constrained feedback stabilizing control is considered for a nonlinear system affine in scalar control. The basic idea is that the resulting closed-loop system has the possibly largest region of attraction of the equilibrium entirely embedded to a domain assigned by state constraints. Unlike well-known approaches based on the methods of optimal control or dynamical programming, the method proposed does not involve an optimization of any cost functional.